Maintenance Supplier Selection: Evaluating the Effect of ...

Advances in Industrial Engineering, Summer 2020, 54(3): 333-354

DOI: 10.22059/jieng.2021.325140.1771

RESEARCH PAPER

Maintenance Supplier Selection: Evaluating the Effect

of Maintenance and Sourcing Strategies

Mohammaad Sheikhalishahi*, Erfan Atri, Amirhossein Radman-Kian, Soroush

Sabaei

School of Industrial and Systems Engineering, College of Engineering, University of Tehran, Tehran,

Iran.

Received: 06 June 2021, Revised: 20 June 2021, Accepted: 20 June 2021

© University of Tehran 2020

Abstract

The advent of globalization and outsourcing of products and services has resulted

in more networked, highly dependent firms in supply chains; so supply chains’

vulnerability to several risks such as equipment breakdown is increased. Although

optimizing maintenance supplier selection has a vital role in supply chain

performance, it has not received enough attention in the literature. Due to the effect

of maintenance strategies and supplier selection approaches, in this paper, three

scenarios are considered based on various strategies as follows: 1-Preventive

Maintenance with single supplier selection (PMs), 2- Preventive Maintenance with

multiple supplier selection (PMm), and 3-Condition Based Maintenance with

multiple supplier selection (CBMm). A fuzzy goal programming approach is applied

to make trade-offs between several objectives. The efficacy of the model is

validated through numerical examples, and results are compared to investigate the

effect of implementing each scenario. The results show that in situations that

reducing unreliability cost has higher priority for a decision-maker, CBMm is more

efficient than other scenarios.

Keywords: Supplier Selection;

Maintenance;

Risk Management;

Life Cycle Costing;

Fuzzy Goal Programming

Introduction

With the advent of globalization and the emergence of interdependent organizations, the

importance of supplier evaluation and selection has been increased [1]. Therefore, in this

competitive environment optimizing supplier partner selection, which has a significant effect

on firms’ success, is inevitable. Supply chain management (SCM) aims to minimize overall

costs across the system by controlling transaction flows through the whole supply chain [2].

Both academics and professionals have dealt with supplier selection as a theoretical and

practical issue [3] and have emphasized the importance of the supplier selection process [4]–

[7]. Moreover, the advantages of using a systematic approach to select the suppliers are

emphasized in some researches [8], [9].

Despite all the advantages cited, the implementation of SCM’s principles results in more

networked, highly dependent organizations. In other words, organizations are vulnerable to

risks that arise from the problems of coordinating supply and demand, and risks that arise from

disruptions to normal activities [10]–[12]. Disruption events can affect the performance of the

supply chain, and enterprises should be able to deal with such events. Accordingly, dealing with

supply chain risks considerably take into consideration in recent years. Supplier selection and

* Corresponding author: (M. Sheikhalishahi)

Email: [email protected]

334 Sheikhalishahi et al.

evaluation models mainly use acquisition costs as the primary criterion for solving problems,

but this approach to decision-making only attempts to save money in a short time. Life Cycle

Costing (LCC) is an approach that includes the cost of acquisition, ownership, and disposal of

the product/service [13]. LCC is usually defined as all the costs associated with a product

through its operational life [14]. Operating and Maintenance costs (i.e., the ownership cost)

have a significant effect on the supplier selection problem. Subsequently, the decisions about

supplier selection may affect the performance of an organization.

Furthermore, maintenance strategy selection plays a significant role in the maintenance

supplier selection process [15]. The applied maintenance strategy may affect several factors in

manufacturing systems, such as demand for parts, system reliability, and total costs. So, it is

essential to select the proper maintenance strategy and supplier selection process to have a

successful system. There are different maintenance strategies which are explained in short as

follows [16]. Corrective maintenance is unscheduled maintenance used for equipment after

equipment breaks down or malfunctions. Preventive Maintenance (PM), on the other hand, is

scheduled maintenance carried out routinely at pre-determined intervals. Conditioned-Based

Maintenance (CBM) is proposed to increase the effectiveness of preventive maintenance. CBM

decisions are based upon measures of the condition of a system that is obtained over time [17],

[18]. In other words, CBM is a maintenance strategy where maintenance activities are

performed in response to a significant deterioration observed by a change in a monitored

parameter of the machine condition. With technological advancement, maintenance sensors

such as vibration sensors, flow sensors, and photoelectric sensors are becoming more accurate

and reliable. Furthermore, data collection, data analysis, and decision support capabilities for

large datasets are possible with the advent of emerging Information Communication

Technologies [19]. For advantages such as cost reduction by unnecessary maintenance

elimination and more efficient maintenance, CBM implementation in industries has been

increased. Studies have proven that the CBM strategy can be useful in reducing the costs

associated with maintenance, thereby minimizing the occurrence of serious faults [20]. Recent

studies in this area attempt to present SCM models that consider different SCM’s criteria

simultaneously, such as purchasing, production, and distribution [21]. Ristono et al. [22] used

statistical multi-criteria decision making (S-MCDM) methods to propose criteria design

methods for the selection of suppliers, which provide ongoing guidance and avenues for further

researches.

Numerous investigations have focused on the number of simultaneous suppliers for the same

product. Some maintenance managers prefer a single supplier strategy. This strategy is popular

among managers who prefer a lower initial prices and ongoing costs to disruption risks [23].

Moreover, it forms long term-relationship, a significant commitment of the supplier for

maintaining equipment, and lower wholesale price. As the total life cycle costs play a significant

role in SCM, this study intends to examine the effects of various maintenance and supply

selection strategies upon the total life cycle costs. To do so, we define three scenarios and

compare total LCC. All in all, these scenarios are composed of 1. Preventive Maintenance with

single supplier selection (PMs), 2. Preventive Maintenance with multiple supplier selection

(PMm), and 3. Condition Based Maintenance with multi-supplier selection (CBMm).

This study aims to deal with two general concepts in (SCM), including supplier chain risks

and partner selection. In the following subsections, these two concepts are reviewed.

Supply chain and risk

Several studies have investigated supply chain disruption risks and their impact using different

approaches such as risk modeling [24]–[27] and risk mitigation [28]–[32]. Fagundes et al. [33]

classified risk decision support models into three groups and determined six current clusters of


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researches. Supply chain disruption literature is divided into quantitative and qualitative

researches [34]. Recent studies of supply chain management focused on coordination schemes.

Revenue-sharing contracts among supply chain participants have become popular [35]. Song

and Gao [36] proposed two green supply chain game models under revenue-sharing contracts

to improve the greening level of the products and the overall profitability of the supply chain.

Disruption management is a new field in the study of supply chain management. For the first

time, Clausen et al. [37] introduced the concept of disruption management and applied it

successfully in airline operations. Qi et al. [38] investigated demand disruption’s impact on

supply chain coordination. They introduced a quantity discount contract to coordinate a two-

stage supply chain with one manufacturer and one retailer. Yu and Goh [39] explored the effects

of Supply Chain Visibility (SCV) and Supply Chain Risk (SCR) on supply chain performance.

SCV is related to the capability of sharing timely and accurate information on demand,

inventory, transportation cost, and other activities through the supply chain. SCR can be defined

as the probability of an event and its consequences during a specific period through a supply

chain. They used a fuzzy multi-objective decision-making approach to model SCV and SCR to

maximize SCV and Minimize SCR and costs. DuHadway et al. [40] provided a framework for

the detection of disruption sources such as intentional or inadvertent acts. Finally, they proposed

corrective actions for mitigating disruption consequences based on the intent and the source of

the disruption. Lee and Michael [41] presented strategies for reducing vulnerability to security

losses that may cause disruptions. Kleindorfer and Saad [10] proposed a model to estimate and

reduce the outcomes of disruptions, which may arise from natural disasters, strikes, and

economic disruptions. Some studies have developed frameworks to test the threat of potential

disruption on the supply chain process [42]–[44]. They focused on potential mitigation and

supply chain design strategies that can mitigate these disruptions and consequences.

Partner selection

Partner selection is a vital step in the formation of any supply chain [45]. Supplier selection has

received particular attention due to its critical effect on successful supply chain management.

Jain et al. [46] reviewed the main approaches to supplier-related issues based on a summary of

existing research before 2007. Glock et al. [47] conducted a systematic literature review with

a focus on decision support models for partner selection problem. Ho et al. [48] analyzed multi-

criteria decision making (MCDM) approaches for supplier selection based on journal articles

from 2000 to 2008. Ocampo et al. [49] reviewed different partner selection methods in the

supply chain such as multi-criteria decision-making, fuzzy decision-making, artificial

intelligence, mathematical programming, and statistical models from 2006 to 2016. Lin and

Kuo [50] introduces a method named MCB (Multiple Comparisons with the Best), which uses

suppliers’ capabilities such as precision, loss, and accuracy to identify the best supplier and

measure its superiority over other suppliers. Huang et al. [51] developed a two-stage selection

framework based on the factors affecting the partner selection process. They defined practical

factors in the partner selection process as hard and soft factors. In the first stage, they

determined potential partner candidates. Then, in the second stage, they assess candidate

partners' cooperation ability. Çebi and Otay [52] also presented a two-stage framework for

partner selection. The first stage is evaluating and selecting suppliers, and the second is

determining the number of orders allocated to selected suppliers.

Supplier selection techniques have a different amount of complexity and accuracy. There are

three different groups of techniques [3]. The first consists of supplier selection techniques with

low complexity and accuracy, including the Scoring Model (SM) and the Categorical Methods

(CMs). The second group encompasses supplier selection techniques with medium accuracy

and complexity, including the Analytic Network Process (ANP), Analytic Hierarchy Process


(AHP), and Data Envelopment Analysis (DEA). The third one consists of supplier selection

techniques with high complexity and accuracy, including the Fuzzy Set Theory (FST),

Mathematical Programming (MP), and Total Cost of Ownership (TCO) models. Chai and Ngai

[53] reviewed decision-making techniques in supplier selection problem and categorized them

into three main groups: Multi-Criteria Decision Making (MCDM) techniques, Mathematical

Programming (MP) techniques, Data Mining, and Artificial Intelligence (DMAI) techniques.

Although there are many studies in the literature on supplier selection and order allocation

problems, they generally focused on purchasing parts that are used in the manufacturing system

to create final products, not on those used for maintenance of production machinery. Therefore,

it could be deduced that maintenance supplier selection has not received considerable attention

yet. Also, the effect of maintenance strategy and sourcing policy on supplier selection has not

been considered. To fill these gaps, this study aims to make a comparison between PMs, PMm,

and CBMm as a variety of maintenance strategies in the supplier selection process by

considering single and multiple sourcing l6 options.

Problem description

The maintenance supplier selection and order allocation models aim to assist the decision-

maker in choosing the best maintenance supplier and determining the quantity order of each

part. In order to compare mentioned scenarios, identical objective functions are defined for each

of them, while the objective functions aim to minimize purchasing cost, risk measure, downtime

cost, and unreliability cost of the production system simultaneously. Since CBM scenario bears

a time dimension, it is necessary for PM scenarios to consider the demand of each period equal

to that of the first period. In the following sections, three scenarios are explained covering two

maintenance policies (PM and CBM) and two sourcing strategies (single and multiple). For

CBM policy, multiple sourcing is more applicable, and therefore, single sourcing is not

considered.

Scenario 1 (PMs)

The following assumptions are considered:

• Each procured part has a deterministic demand rate (i.e., a given demand per

period) and regularly replace in a pre-defined time interval.

• Because of the unusual situation of manufacturers (such as economic sanctions

impact), lead times are considerable.

• There are several pre-qualified suppliers for each part.

• A multi-period time horizon is considered.

• Because of the nature of the PM strategy, equal demand is considered for each

period.

• Medium/long-term contracts are taken into account, and the choice of the

supplier is fixed for a reasonable period.

• Historical data for suppliers, parts, and criteria are available.

• It is assumed that the cost associated with each unit of uncertainty is constant.

Therefore, the cost coefficients are not incorporated in the formulation of

uncertainty cost.

• Manufacturing, disposal, discount rate, and information costs are assumed to be

the same for all suppliers and consequently have no significant effect on the

supplier selection problem.

• Stocking cost is also not considered in the model because it is assumed that the

total number of parts is ordered according to pre-determined demand, and it is


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independent of the suppliers. In other words, stocking cost is equal for all of the

suppliers.

• Operation and maintenance costs include the cost of installation and costs

associated with the reliability and maintainability of the equipment.

• Uncertainty cost is defined as the summation of those costs related to the risks

of different phases of the supply chain.

• Each equipment’s part in each period must be purchased from only one supplier.

The following notations have been used for the model formulations:

Table 1. Indices and parameters of the basic model

Indices

𝑖 Index of suppliers, 𝑖 = 1, … , 𝐼

𝑗 Index of equipment, 𝑗 = 1, … , 𝐽

𝑘 Index of each part of equipment, 𝑘 = 1, … , 𝐾

Input parameters

𝐶𝑖𝑗𝑘0 Purchasing cost for part 𝑘 of equipment 𝑗 supplied by supplier 𝑖

𝑁𝑅𝑖𝑗𝑘𝑡 The number of repairs for part 𝑘 of equipment 𝑗 supplied by supplier 𝑖 in period 𝑡

𝑀𝑇𝑇𝑅𝑖𝑗𝑘 Mean time of repair for part 𝑘 of equipment 𝑗 supplied by supplier 𝑖

𝐶𝑖𝑗𝑘 Repair cost for part 𝑘 of equipment 𝑗 supplied by supplier 𝑖

𝑅𝑡 System reliability in period 𝑡

𝐶𝑎𝑝𝑖 Capacity of the supplier 𝑖 𝐷𝑗𝑘𝑡 Demand rate for part 𝑘 of equipment 𝑗 in period 𝑡

𝑑𝑡𝑖𝑗𝑘 Delivery time of part 𝑘 of equipment 𝑗 supplied by supplier 𝑖

𝐷𝑇𝑗𝑘 Maximum accepted lead time for part 𝑘 of equipment 𝑗

𝑡𝑑𝑖𝑗𝑘 Downtime of part 𝑘 of equipment 𝑗 supplied by supplier 𝑖

𝑇𝐷𝑗 Maximum accepted downtime of equipment 𝑗

𝑅𝐼𝑖 The risk value of selecting 𝑖th supplier

𝐶𝑈𝑅 Cost of unreliability

Basic problem variables are denoted in Table 2:

Table 2. Variables of the basic model

Decision Variables

𝑞𝑖𝑗𝑘𝑡 Purchasing quantity of part 𝑘 of equipment 𝑗 supplied by supplier 𝑖 in period 𝑡

𝑥𝑖𝑗𝑘𝑡 1, if 𝑞𝑖𝑗𝑘 > 0, 0 otherwise

According to the above notations, the basic model are as follows: Objective functions:

min 𝑍1 = ∑ ∑ ∑ ∑ 𝐶𝑖𝑗𝑘0 . 𝑞𝑖𝑗𝑘𝑡

𝐾

𝑘=1

𝐽

𝑗=1

𝐼

𝑖=1

𝑇

𝑡=1

(1)

min 𝑍2 = ∑ ∑ ∑ ∑ 𝑞𝑖𝑗𝑘𝑡 . 𝑅𝐼𝑖

𝐾

𝑘=1

𝐽

𝑗=1

𝐼

𝑖=1

𝑇

𝑡=1

(2)

min 𝑍3 = ∑ ∑ ∑ ∑ 𝐸(𝑁𝑅𝑖𝑗𝑘𝑡). 𝑀𝑇𝑇𝑅𝑖𝑗𝑘 . 𝐸(𝐶𝑖𝑗𝑘). 𝑞𝑖𝑗𝑘𝑡

𝐾

𝑘=1

𝐽

𝑗=1

𝐼

𝑖=1

𝑇

𝑡=1

(3)


min 𝑍4 = ∑(1 − 𝑅𝑡). 𝐶𝑈𝑅

𝑇

𝑡=1

(4)

Subject to:

∑ ∑ 𝑞𝑖𝑗𝑘𝑡 ≤ 𝐶𝑎𝑝𝑖

𝐾

𝑘=1

𝐽

𝑗=1

∀ 𝑖, 𝑡 (5)

∑ 𝑞𝑖𝑗𝑘𝑡 ≥ 𝐷𝑗𝑘𝑡

𝐼

𝑖=1

∀ 𝑗, 𝑘, 𝑡 (6)

∑ ∑ 𝑡𝑑𝑖𝑗𝑘 . 𝑥𝑖𝑗𝑘𝑡 ≤ 𝑇𝐷𝑗

𝐾

𝑘=1

𝐼

𝑖=1

∀ 𝑗 , 𝑡 (7)

𝑑𝑡𝑖𝑗𝑘 . 𝑥𝑖𝑗𝑘𝑡 ≤ 𝐷𝑇𝑗𝑘 ∀ 𝑖, 𝑗, 𝑘, 𝑡 (8)

𝑥𝑖𝑗𝑘𝑡 ≤ 𝑞𝑖𝑗𝑘𝑡 ∀ 𝑖, 𝑗, 𝑘, 𝑡 (9)

𝑀. 𝑥𝑖𝑗𝑘𝑡 ≥ 𝑞𝑖𝑗𝑘𝑡 ∀ 𝑖, 𝑗, 𝑘, 𝑡 (10)

∑ 𝑥𝑖𝑗𝑘𝑡 = 1𝐼

𝑖=0 ∀ 𝑗, 𝑘, 𝑡 (11)

𝑥𝑖𝑗𝑘𝑡 є {0,1} ∀ 𝑖, 𝑗, 𝑘, 𝑡 (12)

𝑞𝑖𝑗𝑘𝑡 ≥ 0 ∀ 𝑖, 𝑗, 𝑘, 𝑡 (13)

Eqs. 1 to 4 are the objective functions that minimize purchasing cost, risk measure, downtime

cost, and unreliability cost of the production system, respectively. Constraint (5) guarantees that

the quantity of products ordered from each supplier does not exceed its capacity. Constraint (6)

ensures that the demand for each part is satisfied by suppliers. Constraint (7) assures that the

total downtime of each part should be less than the maximum accepted downtime of that part.

In constraint (8), if a part is purchased from a supplier, its delivery time should be less than the

maximum accepted delivery time. Constraints (9) and (10) present the relation between

𝑥𝑖𝑗𝑘𝑡 and 𝑞𝑖𝑗𝑘𝑡. Constraint (11) demonstrates each part must be provided by only one specific

supplier. Finally, Eqs. 12 and 13 are non-negativity and integrality formulas.

Scenario 2 (PMm)

This scenario is identical to PMs, but then again, in PMm supply managers are allowed to divide

purchasing quantity order between different maintenance suppliers—that is—a multi-sourcing

strategy is used to satisfy the demand of each part. Therefore, all constraints and assumptions

of the PMs model are still valid apart from constraint (11) and the last assumption.


339

Scenario 3 (CBMm)

Since the issue of inventory management is very important in this scenario, storage cost must

be added to the objective function. As mentioned before, because the amount of the order in

each period is different according to the inspections, the cost of ordering for each period must

also be considered. New required parameters and variables are defined as follows:

Table 3. New parameters and variables

Input parameters

𝐼𝑖𝑗𝑘𝑡 Mean inventory for part 𝑘 of equipment 𝑗 supplied by supplier 𝑖 in period 𝑡

𝑆𝑗𝑘 Ordering cost for part 𝑘 of equipment 𝑗

𝛽 storage cost coefficient

Problem Variables

𝑞𝑖𝑗𝑘𝑡 Purchasing quantity of part 𝑘 of equipment 𝑗 supplied by supplier 𝑖 in period 𝑡

𝑋𝑖𝑗𝑘𝑡 1, if 𝑞𝑖𝑗𝑘𝑡 > 0, 0 otherwise

𝑁𝑆𝑗𝑘𝑡 The number of the ordering of part 𝑘 of equipment 𝑗 in period 𝑡

The first term, storage cost, is calculated as follows:

∑ ∑ ∑ ∑ 𝐼𝑖𝑗𝑘𝑡 . 𝛽. 𝐶𝑖𝑗𝑘0

𝑇

𝑡=1

𝐾

𝑘=1

𝐽

𝑗=1

𝐼

𝑖=1

Where β is the identical storage cost coefficient for all parts of all equipment and then 𝛽. 𝐶𝑖𝑗𝑘0

is the storage cost per unit in each period. The second term, ordering cost, is calculated as

follows:

∑ ∑ ∑ ∑ 𝑆𝑗𝑘 . 𝑁𝑆𝑗𝑘𝑡

𝑇

𝑡=1

𝐾

𝑘=1

𝐽

𝑗=1

𝐼

𝑖=1

These two new objective functions are added to the first previous objective function (𝑍1).

According to the aforementioned expressions, the new model is developed as follows:

Objective functions:

min 𝑍1 = ∑ ∑ ∑ ∑(𝐶𝑖𝑗𝑘0 . 𝑞𝑖𝑗𝑘𝑡

𝑇

𝑡=1

𝐾

𝑘=1

𝐽

𝑗=1

𝐼

𝑖=1

) + (𝐼𝑖𝑗𝑘𝑡 . 𝛽. 𝐶𝑖𝑗𝑘0 ) + (𝑆𝑗𝑘 . 𝑁𝑆𝑗𝑘𝑡) (14)

min 𝑍2 = ∑ ∑ ∑ ∑ 𝑞𝑖𝑗𝑘𝑡 . 𝑅𝐼𝑖

𝑇

𝑡=1

𝐾

𝑘=1

𝐽

𝑗=1

𝐼

𝑖=1

(15)

min 𝑍3 = ∑ ∑ ∑ ∑ 𝐸(𝑁𝑅𝑖𝑗𝑘𝑡). 𝑀𝑇𝑇𝑅𝑖𝑗𝑘 . 𝐸(𝐶𝑖𝑗𝑘). 𝑞𝑖𝑗𝑘𝑡

𝑇

𝑡=1

𝐾

𝑘=1

𝐽

𝑗=1

𝐼

𝑖=1

(16)

min 𝑍4 = ∑(1 − 𝑅𝑡). 𝐶𝑈𝑅

𝑇

𝑡=1

(17)

S.t constraints (5-10, 12, 13), and:

𝑁𝑆𝑗𝑘𝑡 = ∑ 𝑥𝑖𝑗𝑘𝑡

𝐼

𝑖=1

∀ 𝑗, 𝑘, 𝑡 (18)


𝐼𝑖𝑗𝑘𝑡 =𝑞𝑖𝑗𝑘𝑡

2 ∀ 𝑖, 𝑗, 𝑘, 𝑡 (19)

Eqs. 14 to 17 are the objective functions and total purchasing cost—including storage and

ordering cost—risk measure, downtime cost, unreliability cost of the production system,

respectively. In constraint (18), the number of ordering each part to the suppliers is calculated.

Constraint (19) denotes that the average amount of inventory is equal to the number of

corresponding parts divided by 2. It should be noted that ordering and storage costs are also

incorporated in two other scenarios, but for them the cost values are constant. It is assumed that

whenever the condition of the equipment is degraded, and therefore we have to replace it, the

replacement action will be delayed to the end of the current period.

Illustrative examples

To demonstrate the validity and reliability of the proposed model, a petrochemical case study

is considered. Due to the fact that some required data is missed, some parameters are randomly

generated. In this example, the system of production has three main sub-systems or more

specific equipment. Each piece of equipment involves three parts that could be supplied by

three suppliers. The planning horizon is a multi-period, so 𝑡 ∈ {1,2,3}. The system works

correctly if at least one piece of equipment of each type (1, 2, or 3) works flawlessly. Therefore,

by applying the Universal Generating Function (UGF) technique [54], the total reliability of the

system is calculated as follows:

𝑅𝑡 = (∑ 𝑃𝑗1𝑡 . (𝑃𝑗2𝑡2 + 2𝑃𝑗2𝑡 . (1 − 𝑃𝑗2𝑡)) . (𝑃𝑗3𝑡

3 + 3(1 − 𝑃𝑗3𝑡).

3

𝑗=1

𝑃𝑗3𝑡2 + 3(1 − 𝑃𝑗3𝑡)

2. 𝑃𝑗3𝑡))/3 (20)

Which, 𝑃𝑗𝑘𝑡 indicates the weighted reliability of the 𝑘𝑡ℎ part of the 𝑗𝑡ℎ equipment in period 𝑡.

The reliability of each part is dependent on the respective suppliers, so it is computed as a

weighted average:

𝑃𝑗𝑘𝑡 = ∑ 𝑃𝑟𝑖𝑗𝑘 . 𝑞𝑖𝑗𝑘𝑡/𝐷𝑗𝑘𝑡

𝑛𝑗

(21)

Where, 𝑃𝑟𝑖𝑗𝑘 denotes the reliability of the 𝑘𝑡ℎ part of the 𝑗𝑡ℎ equipment supplied by 𝑖𝑡ℎ supplier.

In this section, numerical examples are proposed to demonstrate the validity and applicability

of the developed model. Three examples are presented in the next section. The first one belongs

to the PMs, the second one is concerned with PMm, and the last one is about the CBMm scenario.

Finally, the results of each scenario are presented to have a comparative study among them.


341

Example one: PMs

Because of using PM as a maintenance strategy in this scenario, the demands are the same in

each period. It is worth noting that 𝐶𝑈𝑅 = 15. Moreover, only one supplier could be selected to

provide the demand for each part.

Table 4. Demand of products in periods

𝐷𝑗𝑘𝑡 Period 1, Parts Period 2, Parts Period 3, Parts

1 2 3 1 2 3 1 2 3

Equipment

1 80 120 60 80 120 60 80 120 60

2 120 60 40 120 60 40 120 60 40

3 80 40 120 80 40 120 80 40 120

Example two: PMm

In the PMm scenario, the demand for products in all periods is precisely as identical as the ones

in PMs. The other parameters of both PMs and PMm, including suppliers capacity, and Suppliers

delivery time are presented in appendix I.

Example three: CBM

In the previous scenario, all parameters and assumptions are the same as the basic model except

for the planning horizon. In the CBM strategy, the demands are different in each period.

Besides, in this scenario, the ordering cost for part 𝑘 of equipment 𝑗 is added and 𝛽 = 0.2. Table

5 shows the demand for each part for different periods.

Table 5. Demand of products in periods

𝐷𝑗𝑘𝑡 Period 1, parts Period 2, parts Period 3, parts

1 2 3 1 2 3 1 2 3

Equipment

1 80 120 60 85 115 60 84 120 53

2 120 60 40 117 53 47 124 53 41

3 80 40 120 83 34 121 84 41 120

The ordering cost of each equipment parts is shown in Table 6.

Table 6. Ordering cost of products

𝑆𝑗𝑘 Parts

1 2 3

Equipment

1 50 45 40

2 55 50 45

3 60 55 50

As mentioned, these values are the constants for other scenarios. The other parameters are

presented in Appendix.


Results and discussion

The Fuzzy Goal Programming (FGP) approach can be applied in order for supply chain

management to attain a compromise solution for multi-objective problems. In order to apply

FGP to solve the models, aspiration levels of each objective are calculated. Then, considering

300000, 5000, 300000, and 10—respectively—as Upper tolerance limit for 𝑍1 to 𝑍4 and 𝜆 =0.5, the amounts of the objective function for FGP and also order quantities are calculated. The

models are coded in GAMS software, and the results for the examples are shown in the

following tables. Table 7 indicates the aspiration level of each objective.

Table 7. Aspiration levels of objective functions

Objective Aspiration Level

PMs PMm CBMm

Purchasing, ordering and storage cost 𝑍1 287566.2 257742 288514.15

Risk of purchasing cost 𝑍2 469.998 469.798 468.609

Downtime cost 𝑍3 266104.92 268144.8 268133.7

Unreliability cost of the system 𝑍4 0.881 0.909 0.901

For calculating the aspiration level of each objective, the corresponding single-objective

model subject to all constraints was solved separately. Table 8 shows the objective function

values of the FGP model.

Table 8. Results of the fuzzy goal programming model

Objective Optimum Value

PMs PMm CBMm

FGP 4.212 4.754 3.355

𝜇𝑧1 0.606 0.985 0.472

𝜇𝑧2 0.956 0.992 0.974

𝜇𝑧3 0.606 0.952 0.023

𝜇𝑧4 0.606 0.585 0.753

Table 8 denotes the value of the fuzzy goal programming model objective functions. It is

noted that the fuzzy goal programming model aims to maximize the FGP value, which leads to

minimizing 𝑍1, 𝑍2, 𝑍3, and 𝑍4 values. The results show the capability of the proposed model

for solving the maintenance supplier selection problem while considering the LCC and supply

chain risks. Order quantities for each scenario are presented in Tables 9 to 11 for PMs, PMm,

and CBMm scenarios, respectively.

In line with Table 9, as expected, each part purchased from only one maintenance supplier,

and demands in all periods are satisfied.


343

Table 9. Order quantities for PMs

Supplier 1 Supplier 2 Supplier 3

𝑞𝑗1 𝑞𝑗2 𝑞𝑗3 𝑞𝑗1 𝑞𝑗2 𝑞𝑗3 𝑞𝑗1 𝑞𝑗2 𝑞𝑗3 P

erio

d 1

𝑞1𝑘 80 - - - 120 60 - - -

𝑞2𝑘 - - - 120 60 - - - 40

𝑞3𝑘 - - 120 80 - - - 40 -

Per

iod

2

𝑞1𝑘 85 - - - - 60 - 115 -

𝑞2𝑘 - - - 117 53 - - - 47

𝑞3𝑘 83 - 121 - 34 - - - -

Per

iod

3 𝑞1𝑘 84 - 53 - - - - 120 -

𝑞2𝑘 124 - - - 53 - - - 41

𝑞3𝑘 84 - 120 - 41 - - - -

Table 10. Order quantities for PMm

According to Table 10, all demands are satisfied, and some of them, such as D121 and D211,

are provided from different suppliers.

Table 11. Order quantities for CBMm


𝑞𝑗1 𝑞𝑗2 𝑞𝑗3 𝑞𝑗1 𝑞𝑗2 𝑞𝑗3 𝑞𝑗1 𝑞𝑗2 𝑞𝑗3

Per

iod

1

𝑞1𝑘 80 20 - - 100 60 - - -

𝑞2𝑘 100 - - 20 60 - - - 40

𝑞3𝑘 80 - 20 - 40 - - - 100

Per

iod

2

𝑞1𝑘 85 15 - - 100 60 - - -

𝑞2𝑘 100 - - 17 53 - - - 47

𝑞3𝑘 83 - 21 - 34 - - - 100

Per

iod

3 𝑞1𝑘 84 20 - - 100 53 - - -

𝑞2𝑘 100 - - 24 53 - - - 41

𝑞3𝑘 84 - 20 - 41 - - - 100


𝑞𝑗1 𝑞𝑗2 𝑞𝑗3 𝑞𝑗1 𝑞𝑗2 𝑞𝑗3 𝑞𝑗1 𝑞𝑗2 𝑞𝑗3

Per

iod

1

𝑞1𝑘 80 20 - - 100 60 - - -

𝑞2𝑘 100 - - 20 60 - - - 40

𝑞3𝑘 80 - 20 - 40 - - - 100

Per

iod

2

𝑞1𝑘 60 20 - 20 100 60 - - -

𝑞2𝑘 90 - - 30 60 10 - - 40

𝑞3𝑘 80 - 30 - 40 - - - 90

Per

iod

3 𝑞1𝑘 80 20 20 - 100 40 - - -

𝑞2𝑘 100 20 - 20 40 - - - 40

𝑞3𝑘 80 - 40 - 40 - - - 80


According to Table 11, demands in all periods are satisfied, and they are also provided from

different suppliers, and suppliers contribute to providing demands.

Comparative results

The comparative results are shown in Table 12 and Figs. 1 to 6.

Table 12. Summary of results

Value PMs PMm CBMm

FGP 4.212 4.7535 3.3545

𝜇𝑧1 0.606 0.985 0.472

𝜇𝑧2 0.956 0.992 0.974

𝜇𝑧3 0.606 0.952 0.023

𝜇𝑧1 0.606 0.585 0.753

Fig. 1. Values for FGP

Since the FGP is a compromised value for multi objective models, it can be considered as a

suitable criterion for organizations to choose proper maintenance strategy with multi-objective

functions. According to Fig. 1, PMm is the strategy which has the highest FGP value. Therefore,

PMm can be taken into account as an appropriate approach for the case study. Note that in

different scenarios, other maintenance strategies may be selected as the preferred one.


345

Fig 2. Values for purchasing, ordering and storage cost (μZ1)

As Fig. 2 demonstrates, for companies where total purchasing cost (μz1) is more important

than other measures, the PMm strategy provides better results. PMs and CBMm are respectively

in the next ranks.

Fig. 3. Values for risk of purchasing cost (μZ2)

On the other hand, Fig. 3 shows that, in preventive maintenance approach, by choosing

multiple sourcing strategy rather than single sourcing, the risk measure criterion is improved

by 0.046. Thus, referring to risk measure objective function, multiple sourcing strategy should

be preferred instead of single sourcing strategy.


Fig. 4. Values for downtime cost (μZ3)

Fig. 4 illustrates that multiple sourcing strategy also can bring about notable enhancement

in terms of downtime cost.

Fig. 5. Values for unreliability cost of the system (μZ4)

According to Fig. 5, the fourth objective (unreliability costs) is the only criterion in which

PMm is not superior to other strategies. CBMm is the preferable strategy to cope with the

unreliability cost of the production system. Ultimately, in the industries in which the importance

of unreliability risk of system outweighs other objective functions, supply chain managers may

would rather CBM strategy with multiple sourcing policies.


347

Fig. 6. Comparison of three scenarios

Altogether, we can conclude that for the proposed case study, PMm is the preferred strategy.

Noteworthy to mention if we consider various weights for objective functions, other

maintenance strategies and sourcing policies may be selected as an optimum one.

Conclusion

In this paper, a maintenance supplier selection problem that considers total cost (including

storage and ordering cost), risk measure, downtime cost, and unreliability cost of the production

system is addressed. In the proposed model, the manufacturing system consists of some

different multi-component (part) equipment, and a set of suppliers can provide the required

parts. In order to compare different types of maintenance strategies and sourcing policies, three

scenarios are considered: preventive maintenance with multiple and single supplier and

condition-based maintenance. A multi-period mathematical model is formulated, and FGP is

applied to handle four objective functions. The results show that apart from one of the

objectives—that is unreliability costs—PMm is the recommended strategy for the case study. It

is worth noting that in some industries and plants– for instance, oil and gas, aviation, military

and defense industries, and nuclear power plants – a failure in systems causes irreparable

damage, which leads to considerable cost. This is why supply chain managers of these industries

not only pay particular attention to the system reliability but also set that as the first priority

among all the other objective functions. In the proposed model, the CMB strategy has the best

performance according to the reliability measure. Thus, for future research and in case that one

of the objective functions has higher priority, the weighted sum method can be applied. Also,

uncertainty in determining some parameters, such as demand rate, delivery time, unreliability

cost, and repair cost can be addressed in future studies.


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351

Appendix

Table A.1. Demand of products

𝐷𝑗𝑘 Parts

1 2 3

Equipment

1 80 120 60

2 120 60 40

3 80 40 120

Table A.2. Capacity of the suppliers

Supplier Capacity

1 500

2 450

3 420

Table A.3. Supplier’s delivery time (𝑑𝑡𝑖𝑗𝑘)

𝑑𝑡𝑗𝑘 Supplier 1 Supplier 2 Supplier 3

𝑑𝑡𝑗1 𝑑𝑡𝑗2 𝑑𝑡𝑗3 𝑑𝑡𝑗1 𝑑𝑡𝑗2 𝑑𝑡𝑗3 𝑑𝑡𝑗1 𝑑𝑡𝑗2 𝑑𝑡𝑗3

𝑑𝑡1𝑘 8 7 12 13 10 7 11 17 10

𝑑𝑡2𝑘 9 15 7 10 6 8 6 11 16

𝑑𝑡3𝑘 7 12 16 12 8 8 16 11 10

Maximum accepted delivery time= 16 for all parts

Table A.4. Downtimes (𝑡𝑑𝑖𝑗𝑘)

𝑡𝑑𝑗𝑘 Supplier 1 Supplier 2 Supplier 3

𝑡𝑑𝑗1 𝑡𝑑𝑗2 𝑡𝑑𝑗3 𝑡𝑑𝑗1 𝑡𝑑𝑗2 𝑡𝑑𝑗3 𝑡𝑑𝑗1 𝑡𝑑𝑗2 𝑡𝑑𝑗3

𝑡𝑑1𝑘 14 6 6 15 6 10 7 15 15

𝑡𝑑2𝑘 11 7 8 8 12 9 9 11 6

𝑡𝑑3𝑘 12 15 7 12 14 10 11 13 12

Maximum accepted downtime= (2880,5760, 3760) for equipment


Table A.5. Expected number of repairs (𝐸[𝑁𝑅𝑖𝑗𝑘𝑡])

𝐸[𝑁𝑅𝑗𝑘𝑡] Supplier 1 Supplier 2 Supplier 3

𝑁𝑅𝑗1 𝑁𝑅𝑗2 𝑁𝑅𝑗3 𝑁𝑅𝑗1 𝑁𝑅𝑗2 𝑁𝑅𝑗3 𝑁𝑅𝑗1 𝑁𝑅𝑗2 𝑁𝑅𝑗3

Per

iod

1 𝑁𝑅1𝑘 0.55 0.52 0.49 0.52 0.50 0.48 0.49 0.46 0.43

𝑁𝑅2𝑘 0.51 0.48 0.46 0.49 0.46 0.45 0.46 0.43 0.40

𝑁𝑅3𝑘 0.48 0.46 0.43 0.46 0.44 0.43 0.43 0.40 0.38

Per

iod

2 𝑁𝑅1𝑘 0.54 0.49 0.52 0.50 0.51 0.48 0.43 0.49 0.46

𝑁𝑅2𝑘 0.46 0.51 0.48 0.45 0.49 0.46 0.40 0.43 0.46

𝑁𝑅3𝑘 0.43 0.48 0.46 0.43 0.46 0.44 0.38 0.43 0.40

Per

iod

3 𝑁𝑅1𝑘 0.52 0.50 0.48 0.55 0.52 0.49 0.52 0.50 0.48

𝑁𝑅2𝑘 0.49 0.46 0.45 0.51 0.48 0.46 0.49 0.46 0.45

𝑁𝑅3𝑘 0.46 0.44 0.43 0.48 0.46 0.43 0.46 0.44 0.43

Table A.6. Mean time to repair (𝑀𝑇𝑇𝑅𝑖𝑗𝑘)

𝑀𝑇𝑇𝑅𝑗𝑘 Supplier 1 Supplier 2 Supplier 3

𝑀𝑇𝑇𝑅𝑗1 𝑀𝑇𝑇𝑅𝑗2 𝑀𝑇𝑇𝑅𝑗3 𝑀𝑇𝑇𝑅𝑗1 𝑀𝑇𝑇𝑅𝑗2 𝑀𝑇𝑇𝑅𝑗3 𝑀𝑇𝑇𝑅𝑗1 𝑀𝑇𝑇𝑅𝑗2 𝑀𝑇𝑇𝑅𝑗3

𝑀𝑇𝑇𝑅1𝑘 5.00 4.75 4.50 4.80 4.56 4.42 4.51 4.20 3.90

𝑀𝑇𝑇𝑅2𝑘 4.65 4.42 4.19 4.46 4.24 4.11 4.20 3.90 3.63

𝑀𝑇𝑇𝑅3𝑘 4.40 4.18 3.96 4.22 4.01 3.89 3.97 3.69 3.43

Table A.7. Parts reliabilities (𝑝𝑟𝑖𝑗𝑘)

𝑝𝑟𝑗𝑘 Supplier 1 Supplier 2 Supplier 3

𝑝𝑟𝑗1 𝑝𝑟𝑗2 𝑝𝑟𝑗3 𝑝𝑟𝑗1 𝑝𝑟𝑗2 𝑝𝑟𝑗3 𝑝𝑟𝑗1 𝑝𝑟𝑗2 𝑝𝑟𝑗3

𝑝𝑟1𝑘 0.96 0.69 0.89 0.69 0.92 0.96 0.72 0.83 0.86

𝑝𝑟2𝑘 0.97 0.74 0.70 0.88 0.90 0.77 0.67 0.82 0.87

𝑝𝑟3𝑘 0.93 0.77 0.90 0.82 0.96 0.89 0.91 0.96 0.95

Table A.8. Expected value of the repair cost (𝐶𝑖𝑗𝑘)

𝐶𝑗𝑘 Supplier 1 Supplier 2 Supplier 3

𝐶𝑗1 𝐶𝑗2 𝐶𝑗3 𝐶𝑗1 𝐶𝑗2 𝐶𝑗3 𝐶𝑗1 𝐶𝑗2 𝐶𝑗3

𝐶1𝑘 79 65 53 80 66 57 79 63 50

𝐶2𝑘 78 64 52 79 64 56 77 61 48

𝐶3𝑘 78 63 51 78 64 55 76 60 47


353

Table A.9. Purchasing price (𝐶𝑖𝑗𝑘0 )

𝐶𝑗𝑘0


𝐶𝑗10 𝐶𝑗2

0 𝐶𝑗30 𝐶𝑗1



0 𝐶𝑗30

𝐶1𝑘0 115.9 104.3 93.9 127.5 114.7 103.2 139.0 125.1 112.6

𝐶2𝑘0 127.5 114.7 103.2 140.2 126.2 113.6 153.0 137.7 123.9

𝐶3𝑘0 140.2 126.2 113.6 154.2 138.8 124.9 168.2 151.4 136.3

Table A.10. Weights of risks for each supplier

Risks Supplier

1

Supplier

2

Supplier

3

Supplier bankruptcy 0.06 0.014 0.0056

War and terrorism, man-made disasters 0.0245 0.069 0.02383

Excessive handling due to border crossing or to change in

transportation modes 0.0040 0.022 0.0419

Cost uncertainty 0.0316 0.0128 0.0095

Exchange rate risk 0.0114 0.0577 0.0868

Data information security risks and legal risks 0.0159 0.0618 0.1283

Natural disasters 0.0437 0.0405 0.0206

Total 0.1911 0.2778 0.531


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